A low-energy peak (below 1 eV) is also apparent in Fig. REF  (a). This feature, which has been observed in ab-intio calculations by others [1]}, [2]}, corresponds to a broad shoulder in the EELS, and is due to the low-energy \(\pi \)  \(\rightarrow \)  \(\pi ^{\star }\)  single-particle excitation. Low energy graphene features, including intraband transitions are generally quite dependent upon the value of momentum transfer. [3]} These features are outside the energy regime of interest for the surface and bulk plasmon peaks in this paper, work in which very low-energy excitations are a focus should not neglect momentum transfer dependence. In the context of these calculations, increasing momentum transfer values lead to a shift towards higher energies of the \(\pi \)  plasmons for intrinsic graphene. [2]}, [5]} Others, for example Gao et al.  [5]} have found (via the time-dependent local density approximation) linear dispersion for the \(\pi \)  plasmon (the key feature in our energy regime of interest) in single-layer graphene for both \(\bar{\Gamma }\) -\(\bar{M}\)  and \(\bar{\Gamma }\) -\(\bar{K}\)  directions. The calculations of Gao et al. were found to agree well with experiment.
